Express your answer as a mixed number simplified to lowest terms. $16\dfrac{2}{3}-14\dfrac{14}{17} = {?}$
Solution: Find a common denominator for the fractions: $= {16\dfrac{34}{51}}-{14\dfrac{42}{51}}$ Convert ${16\dfrac{34}{51}}$ to ${15 + \dfrac{51}{51} + \dfrac{34}{51}}$ So the problem becomes: ${15\dfrac{85}{51}}-{14\dfrac{42}{51}}$ Separate the whole numbers from the fractional parts: $= {15} + {\dfrac{85}{51}} - {14} - {\dfrac{42}{51}}$ Bring the whole numbers together and the fractions together: $= {15} - {14} + {\dfrac{85}{51}} - {\dfrac{42}{51}}$ Subtract the whole numbers: $=1 + {\dfrac{85}{51}} - {\dfrac{42}{51}}$ Subtract the fractions: $= 1+\dfrac{43}{51}$ Combine the whole and fractional parts into a mixed number: $= 1\dfrac{43}{51}$